Baseball question from a football/basketball ref.

[stir22]

Hello, my baseball brethren!!!

Was at the ballpark last night watching my local minor league baseball team. Here's the scenario- Home up 4-0, 7th inning, very smooth game. Home team starting pitcher was pitching a masterful game, one hitter at that point. Anyway, one of his pitches got away from him, and went a few inches behind the batter. Clearly did not hit the batter- nothing untoward had happened in the game. The homeplate ump awarded the batter first base. The batter actually argued just a bit, saying the pitch didn't hit him, and he want to stay in the box. The ump insisted he take first base. My question is, is first base awarded automatically for pitches that go behind the batter, regardless of the scenario?

Thanks!!!